C) 41.5 D) 50.9 24 In the xy-plane, the graph of a linear equation of the...
Q2)a) [5pt] Find the equation of the line in the plane (in y = mx +b form) that is perpendicular to the line y = 1/5x + 17 and goes through the point (9, 12). Equation of the line: _______ Q2)b) [5pt] Find the equation of the line in the plane that is perpendicular to the y axis and goes through the point (-2,4). Equation of the line:_______
Solve the following problems. Submit the written solution and a GeoGebra file. A. Determine a vector equation for the plane that contains the following two lines. 11:r = (2,4,-2) + t(1,-1,3), t E R 12:7 = (2, 4,-2) + s(3, 2,-2),s E R (2,4,-2)+11 ',-1,5) +S(5,2,-2) か B. Find the angle between these lines. C. Determine the corresponding Cartesian equation of this plane. D. Determine the distance between point Q(2,2,-1) and Line 1. E. Determine the coordinates of the point...
The polar equation r = θ defines a spiral in the xy-plane. Let C be the portion of this spiral starting at (x, y) = (−3π, 0) and ending at (x, y) = (0, 0). Let F(x, y) = < (y − 1)^e cos(x−xy) sin(x − xy), xe^cos(x−xy) sin(x − xy) > Find Z C F · dr
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
Graph the equation and its tangent. a) Graph y = x3 - 4 and the tangent to the curve at the point whose x-coordinate is 0 and the tangent line to the curve at the point whose x-coordinate is 0. b) What is the equation of the tangent line at x = 0 in slope-intercept form (i.e. y = mx+b)?
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (25 − y2)y' = x2 Choose the right answer and explain a. A unique solution exists in the regions y < −5, −5 < y < 5, and y > 5. b. A unique solution exists in the region y < 5. c. A unique solution exists in the region consisting of...
An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2 - 2t>. (a) Find the position of the object at time t-5. C 3 15 (b) At what time is the object at the point (O, 0)? t- (c) Does the object pass through the point (4, 28)? Yes 0 No (d) Find an equation in x and y whose graph is the path of the object.
C. A 0-kg particle moves in the horizontal xy-plane motion under the action of a net forceEF(A+ 5?) N to a point A in the plane. The position vector from the origin to the point A is r-(-3i-210Dm i. What is the magnitude and direction of the linear momentum, Latt-5s The net moment I, acting on the particle at t-5 s
have In the xy-plane, porns A and B Coordinates sm and Coss), What is the equation of the line that passes through the tin origns andis pendidiciar to the line segment AB Ay=s by=1 (y=x d.g=X45
The equation below gives parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle's path by finding a Cartesian equation for it Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. Fird a Carlesiari equalion for Uhe paricle's path. Graph the Cartesian equation below. Indicate the direction of motion as t increases Choose the comect graph below O A. OD. ов. O C....